Dimensionality reduction is essential for industrial process data with numerous nonlinear variables to retain only the important

features for visualization or subsequent tasks. This study serves as a tutorial demonstrating how various dimensionality 

reduction techniques perform as the complexity of process variables in toy examples increases. Among the variables, there 

are those containing fault signals, aiming to demonstrate the process of performing a fault detection task. The results evaluated

based on three criteria showed that Uniform Manifold Approximation and Projection (UMAP) demonstrated notable 

results, particularly with sparse and noisy data, while also off ering adequate robustness to out-of-sample test data. This tutorial

provides guidance on selecting the appropriate dimensionality reduction technique based on data complexity, ultimately 

enabling more eff ective execution of subsequent tasks.